The most important moment in your case is when you are faced with the decision of whether or not you are going to talk to the police. When you talk to the police, you are establishing your story for the rest of the case. Your statement to police will tie your future lawyer's hands as to what he or she will be able to argue to a future judge or jury on your behalf. Taking advantage of your right to remain silent is paramount to getting on the road to a successful outcome in your case. The police are not your friends when you are the target of an investigation. If you think you can outsmart trained law enforcement officers or detectives, think again. Many times when they are asking you what happened, they know more than you about what happened. True story.
Another factor which is lost within this area of the law is that if it's the FBI or other federal agency that's asking the questions, things get even more complicated. If you lie to them, or if they can prove you lied to them, this will many times result in additional charges which carry prison time. Many a smart defendant has been questioned by the FBI and eventually ended up in federal prison not because of what the original investigation was about, but because they lied during questioning.
Keep your mouth shut and you will be halfway home.